# Find the differential dy for the given values of x and dx. y=frac{e^x}{10},x=0,dx=0.1

Question
Differential equations
Find the differential dy for the given values of x and dx. $$y=\frac{e^x}{10},x=0,dx=0.1$$

2020-10-27
$$y=e^{\frac{x}{10}}$$
Differentiate both sides with respect to x
$$\frac{dy}{dx}=\frac{d(e^{\frac{x}{10}})}{dx}$$
Using chain rule, we can write
$$\frac{dy}{dx}=\frac{d(e^{\frac{x}{10}})}{d(\frac{x}{10})}\cdot\frac{d(\frac{x}{10})}{dx}$$
Recall: $$\frac{d(e^u)}{du}=e^u$$
$$\frac{dy}{dx}=e^{\frac{x}{10}}\cdot\frac{1}{10}$$
$$\frac{dy}{dx}=\frac{e^{\frac{x}{10}}}{10}$$
Multiply both sides by dx
$$dy=\frac{e^{\frac{x}{10}}}{10dx}$$
Result: $$dy=\frac{e^{\frac{x}{10}}}{10dx}$$

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